Brief

Implement a Time Series Forecasting model in Python, by using the FBProphet module. The forecasting model should be able to predict the Sunspots (see below) by using Facebook’s Prophet Time Series Forecasting model. Prophet is a procedure for forecasting time series data based on an additive model where non-linear trends are fit with yearly, weekly, daily seasonality. Sunspots are temporary phenomena on the Sun's photosphere that appear as spots darker than the surrounding areas. They are regions of reduced surface temperature caused by concentrations of magnetic field flux that inhibit convection. Sunspots usually appear in pairs of opposite magnetic polarity. Their number varies according to the approximately 11-year solar cycle. Source: https://en.wikipedia.org/wiki/Sunspot You should test your forecasting model in three (3) distinct datasets. On Daily, Monthly Mean, and Yearly Mean sunspots.

Imports

import pandas as pd
import numpy as np
import seaborn as sns
import matplotlib
import matplotlib.pyplot as plt

from fbprophet import Prophet
from fbprophet.diagnostics import cross_validation
from fbprophet.diagnostics import performance_metrics
from fbprophet.plot import plot_cross_validation_metric

import sklearn
from sklearn.metrics import mean_absolute_error
from sklearn.metrics import mean_absolute_percentage_error
from sklearn.metrics import r2_score

# quick fixes
%load_ext autoreload
import matplotlib.font_manager

The autoreload extension is already loaded. To reload it, use:
  %reload_ext autoreload

Functions

Data loading and processing

# get datetime and move to first
def make_col_datetime(df, freq):
    
    # get datetime features present
    date_features_array = ['Year', 'Month', 'Day']
    for feature in date_features_array:
        if(feature not in df.columns):
            if(feature == 'Day'):
                df.insert(2, feature, 1)
            if(feature == 'Month'):
                df.insert(1, feature, 1)
    
    #make datetime 
    df['Date'] = pd.to_datetime(df[date_features_array])
    df['ds'] = pd.to_datetime(df[date_features_array])
    
    # pop the column 
    first_column = df.pop('Date')

    # insert at first position 
    df.insert(0, 'Date', first_column)
    
    # Set as index
    df = df.set_index('Date')

    # Convert TimeSeries to specified frequency
    df = df.asfreq(freq)

    # sort
    df = df.sort_index()

    return df

# load data
def data_load(name, col_names, freq):
    df = pd.read_csv(r'data/{}.csv'.format(name), names=col_names, header=None, delimiter=';')
    
    df['Year'] = df['Year'].astype(int)
    return make_col_datetime(df, freq)

def quick_look(df):
    display(df.head(5))
    display(df.tail(5))
    display(df.info())
    display(df.describe())

# may want to explore but focuus in on spots and thhey are well represented in whole dataset 
def df_col_value_gt_or_eq(df, col, value):
    df = df[df[col] >= value]
    return df

def handle_missing(df):
    # replace -1 with None 
    df = df.replace(-1, None)
    
    # creating series True or False for NaN data and present data respectively. 
    nul_data = pd.isnull(df['y']) 

    # print only the data, Customers = NaN 
    display(df[nul_data])
    
    # fill the missing data using the of the present observations
    df = df.assign(y = df.y.fillna(df.y.median()))
    
    # creating series True or False for NaN data and present data respectively. 
    nul_data = pd.isnull(df['y']) 

    # print only the data, Customers = NaN 
    display(df[nul_data])
    
    return df

Plots

def simple_plot(df, y):
    font = {'family' : 'Lucida Grande',
            'weight' : 'normal',
            'size'   : 16}
    
    fig, ax = plt.subplots(figsize = (14, 10))
    
    df[y].plot(ax = ax, label = y)
    
    plt.title("{} vs Index(Date)".format(y.capitalize()), 
              fontsize = 22)
    
    matplotlib.rc('font', **font)
    
    ax.legend();

def simple_plot_bulk(df, *argv):
    for arg in argv:
        simple_plot(df, arg)

def namestr(obj, namespace):
    return [name for name in namespace if namespace[name] is obj]

def plot_kde(labels, *argv):    
    plt.figure(figsize=(14, 11))
    sns.set(font_scale = 2)
    for idx, arg in enumerate(argv):
        sns.kdeplot(arg, label=labels[idx])
    plt.legend(prop={'size': 16})

Models

Preprocess

def extract_df(df, feature, name, ds):
    df = df[[ds, feature]]
    df = df.rename(columns={feature: name})
    return df

# Augmented Dickey-Fuller (ADF) Test
# reference: https://www.analyticsvidhya.com/blog/2021/06/statistical-tests-to-check-stationarity-in-time-series-part-1/

# A key point to remember here is: Since the null hypothesis assumes the presence of unit root, that is α=1, the p-value 
# obtained should be less than the significance level (say 0.05) in order to reject the null hypothesis. Thereby, inferring 
# that the series is stationary.

# Load Statsmodels 
import statsmodels.api as sm

# ADF Test
# Function to print out results in customised manner
from statsmodels.tsa.stattools import adfuller

# ADF
def adf_test(timeseries):
    print ('Results of Dickey-Fuller Test:')
    
    dftest = adfuller(timeseries, autolag = 'AIC')
    
    dfoutput = pd.Series(dftest[0:4], index=['Test Statistic','p-value','#Lags Used','Number of Observations Used'])
    
    for key, value in dftest[4].items():
        dfoutput['Critical Value (%s)'%key] = value
        
    print (dfoutput)
    
    print("Conclusion")
    print(dftest[1])
    if(dftest[1] > 0.05):
        print("DO NOT reject the null hypothesis: Non-Stationary")
    else:
        print("Reject the null hypothesis: Stationary")

# Plot and call ADF
def adf_test_show(df, feature):
    # Plotting the Data

    # Define the plot size
    plt.figure(figsize=(16,5))

    # Plot the data
    plt.plot(df.index, df[feature], label = "Sunspot_number")
    plt.legend(loc = 'best')
    plt.title("Sunspot Data")
    plt.show()
    
    adf_test(df[feature])
    

# Kwiatkowski-Phillips-Schmidt-Shin (KPSS) Test

# A key difference from ADF test is the null hypothesis of the KPSS test is that the series is stationary.
# That is, if p-value is < significance level (say 0.05), then the series is non-stationary. Whereas in ADF test, 
# it would mean the tested series is stationary.

# Function to print out results in customised manner
from statsmodels.tsa.stattools import kpss

def kpss_test(timeseries):
    print ('Results of KPSS Test:')
    kpsstest = kpss(timeseries, regression='c', nlags="auto")
    kpss_output = pd.Series(kpsstest[0:3], index=['Test Statistic','p-value','#Lags Used'])
    for key,value in kpsstest[3].items():
        kpss_output['Critical Value (%s)'%key] = value
    print (kpss_output)
    
    print("Conclusion")
    print(kpsstest[1])
    if(kpsstest[1] < 0.05):
        print("Reject the null hypothesis: Non-Stationary")
    else:
        print("DO NOT Reject the null hypothesis: Stationary")
    

def simple_prophet_model(m, df, period_1, period_2, period_3, freq, daily = False, monthly = False):
    
    m
    # instantiate
    m = Prophet(seasonality_mode='multiplicative',
                               seasonality_prior_scale = 20,
                               daily_seasonality=False, 
                               weekly_seasonality=False,
                               yearly_seasonality=False,
                              )


    # add custom seasonality
    m.add_seasonality(name='yearly',
                                     period=365.25,
                                     fourier_order=25)
    
    if(monthly):
        m.add_seasonality(name='monthly',
                                         period=30.5,
                                         fourier_order=55)
    if(daily):
        m.add_seasonality(name='daily',
                                         period=1,
                                         fourier_order=15)
        
    m.add_seasonality(name='11_yearly',
                                     period=4026,
                                     fourier_order=25)

    # fit
    m.fit(df)

    # future dates & forcast & results
    future_dates_1 = m.make_future_dataframe(periods = period_1, freq = freq)
    forcast_1 = m.predict(future_dates_1)
    display(forcast_1.tail())
    fig_1 = m.plot(forcast_1, uncertainty=True)
    # Visualize Each Component (Trend, Seasonality, ...)
    fig_1_1 = m.plot_components(forcast_1)
    ax_1 = fig_1_1.gca()
    ax_1.tick_params(axis="x", labelsize=12)
    ax_1.tick_params(axis="y", labelsize=12)


    future_dates_2 = m.make_future_dataframe(periods = period_2, freq = freq)
    forcast_2 = m.predict(future_dates_2)
    display(forcast_2.tail())
    fig_2 = m.plot(forcast_2, uncertainty=True)
    # Visualize Each Component (Trend, Seasonality, ...)
    fig_2_1 = m.plot_components(forcast_2)
    ax_2 = fig_2_1.gca()
    ax_2.tick_params(axis="x", labelsize=12)
    ax_2.tick_params(axis="y", labelsize=12)

    future_dates_3 = m.make_future_dataframe(periods = period_3, freq = freq)
    forcast_3 = m.predict(future_dates_3)
    display(forcast_3.tail())
    fig_3 = m.plot(forcast_3, uncertainty=True)
    # Visualize Each Component (Trend, Seasonality, ...)  
    fig_3_1 = m.plot_components(forcast_3)
    ax_3 = fig_3_1.gca()
    ax_3.tick_params(axis="x", labelsize=12)
    ax_3.tick_params(axis="y", labelsize=12)
    
    return m, future_dates_1, forcast_1, future_dates_2, forcast_2, future_dates_3, forcast_3

def split(data, steps):
    data_train = data[:-steps]
    data_test  = data[-steps:]

    print(f"Train dates : {data_train.index.min()} --- {data_train.index.max()}  (n={len(data_train)})")
    print(f"Test dates  : {data_test.index.min()} --- {data_test.index.max()}  (n={len(data_test)})")
    
    return data_train, data_test

def plot_test_predict(test, forecast):
    ax = forecast.plot(x = 'ds', y = 'yhat', legend = True, label = 'predictions', figsize = (12,8))
    test.plot(x='ds', y = 'y', legend = True, label = 'True Test Data', ax = ax)

def get_performance_metrics_plot(cv):
    df_pm = performance_metrics(cv)
    df_pm.head()
    
    plot_cross_validation_metric(cv, metric='rmse')
    
    plot_cross_validation_metric(cv, metric='mae')
    
    

def model_with_cv(df, growth, n_changepoints, changepoint_prior_scale, seasonality_prior_scale, freq, 
                  periods, initial, period, horizon, units, monthly=True, daily=False):
    
    # cap
    if(growth == 'logistic'):
        df.loc[:,'cap'] = 500
        df.loc[:,'floor'] = 1
        
    
    # instantiate prophet
    prophet_with_cv = Prophet(growth = growth,
                              n_changepoints = n_changepoints,
                              changepoint_prior_scale = changepoint_prior_scale,
                              seasonality_prior_scale = seasonality_prior_scale, 
                              daily_seasonality=False,
                              weekly_seasonality=False,
                              yearly_seasonality=False)
    
    # add custom seasonality
    prophet_with_cv.add_seasonality(name='yearly',
                                     period=365.25,
                                     fourier_order=25)
    
    if(monthly):
        prophet_with_cv.add_seasonality(name='monthly',
                                         period=30.5,
                                         fourier_order=55)
    if(daily):
        prophet_with_cv.add_seasonality(name='daily',
                                         period=1,
                                         fourier_order=15)
        
    prophet_with_cv.add_seasonality(name='11_yearly',
                                     period=4026,
                                     fourier_order=25)
    
    prophet_with_cv.fit(df)
    
    # future 
    future = prophet_with_cv.make_future_dataframe(freq = freq, periods = periods)
    
    # cap
    if(growth == 'logistic'):
        future.loc[:,'cap'] = 500
        future.loc[:,'floor'] = 1
    
    # predict 
    forcast = prophet_with_cv.predict(future)
    
    # predict cv
    cv_results = cross_validation(prophet_with_cv, 
                                  initial='{} {}'.format(initial, units), 
                                  period='{} {}'.format(period, units), 
                                  horizon = '{} {}'.format(horizon, units)
                                 )

    
    return prophet_with_cv, forcast, cv_results

Daily

Data and brief EDA

Load

# load in dataset
df_daily = data_load("daily", ['Year', 'Month', 'Day', 'Decimal_year', 'Sunspot_number', 'Standard_deviation', 
          'Number_observations', 'Provisional_indicator'], 'D')

# simple & quick EDA
quick_look(df_daily)

# plot target vs index(date)
simple_plot_bulk(df_daily, "Sunspot_number", 'Standard_deviation', 'Number_observations')

	Year	Month	Day	Decimal_year	Sunspot_number	Standard_deviation	Number_observations	Provisional_indicator	ds
Date
1818-01-01	1818	1	1	1818.001	-1	-1.0	0	1	1818-01-01
1818-01-02	1818	1	2	1818.004	-1	-1.0	0	1	1818-01-02
1818-01-03	1818	1	3	1818.007	-1	-1.0	0	1	1818-01-03
1818-01-04	1818	1	4	1818.010	-1	-1.0	0	1	1818-01-04
1818-01-05	1818	1	5	1818.012	-1	-1.0	0	1	1818-01-05

	Year	Month	Day	Decimal_year	Sunspot_number	Standard_deviation	Number_observations	Provisional_indicator	ds
Date
2022-04-26	2022	4	26	2022.316	132	21.8	43	0	2022-04-26
2022-04-27	2022	4	27	2022.319	132	14.8	43	0	2022-04-27
2022-04-28	2022	4	28	2022.322	135	15.5	42	0	2022-04-28
2022-04-29	2022	4	29	2022.325	107	21.4	39	0	2022-04-29
2022-04-30	2022	4	30	2022.327	51	8.3	35	0	2022-04-30

<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 74630 entries, 1818-01-01 to 2022-04-30
Freq: D
Data columns (total 9 columns):
 #   Column                 Non-Null Count  Dtype         
---  ------                 --------------  -----         
 0   Year                   74630 non-null  int64         
 1   Month                  74630 non-null  int64         
 2   Day                    74630 non-null  int64         
 3   Decimal_year           74630 non-null  float64       
 4   Sunspot_number         74630 non-null  int64         
 5   Standard_deviation     74630 non-null  float64       
 6   Number_observations    74630 non-null  int64         
 7   Provisional_indicator  74630 non-null  int64         
 8   ds                     74630 non-null  datetime64[ns]
dtypes: datetime64[ns](1), float64(2), int64(6)
memory usage: 5.7 MB

None

	Year	Month	Day	Decimal_year	Sunspot_number	Standard_deviation	Number_observations	Provisional_indicator
count	74630.000000	74630.000000	74630.000000	74630.000000	74630.000000	74630.000000	74630.000000	74630.000000
mean	1919.665416	6.516522	15.729130	1920.164876	78.580142	6.905413	4.867279	0.998392
std	58.985539	3.449999	8.799916	58.985309	77.303259	4.792459	8.838895	0.040067
min	1818.000000	1.000000	1.000000	1818.001000	-1.000000	-1.000000	0.000000	0.000000
25%	1869.000000	4.000000	8.000000	1869.081750	15.000000	2.900000	1.000000	1.000000
50%	1920.000000	7.000000	16.000000	1920.166500	57.000000	6.500000	1.000000	1.000000
75%	1971.000000	10.000000	23.000000	1971.247250	123.000000	10.000000	1.000000	1.000000
max	2022.000000	12.000000	31.000000	2022.327000	528.000000	77.700000	69.000000	1.000000

Features

'Year' - Year

'Month' - Month

'Day' - Day

'Decimal_year' - Date in fraction of year

'Daily_sunspot_number' - Daily total sunspot number. A value of -1 indicates that no number is available for that day (missing value).

'Standard_deviation' - Daily standard deviation of the input sunspot numbers from individual stations.

'Number_observations' - Number of observations used to compute the daily value.

'Provisional_indicator' - Definitive/provisional indicator. A blank indicates that the value is definitive. A '*' symbol indicates that the value is still provisional and is subject to a possible revision (Usually the last 3 to 6 months)

No null values. Note: the -1 values in Daily_sunspot_number

# if we have the mind to use only records with high number of observations
# df_daily = df_col_value_gt_or_eq(df_daily, 'Number_observations', 1)
# df_daily.head(50)

# distribution of values
plot_kde(['Sunspot_number'], df_daily['Sunspot_number'])

Model

Prep

# extract y
df_daily_model = extract_df(df_daily, 'Sunspot_number', 'y', 'ds')

# take a look at the data
display(df_daily_model.head())
display(df_daily_model.tail())

	ds	y
Date
1818-01-01	1818-01-01	-1
1818-01-02	1818-01-02	-1
1818-01-03	1818-01-03	-1
1818-01-04	1818-01-04	-1
1818-01-05	1818-01-05	-1

	ds	y
Date
2022-04-26	2022-04-26	132
2022-04-27	2022-04-27	132
2022-04-28	2022-04-28	135
2022-04-29	2022-04-29	107
2022-04-30	2022-04-30	51

# median fill
df_daily_model = handle_missing(df_daily_model)

	ds	y
Date
1818-01-01	1818-01-01	None
1818-01-02	1818-01-02	None
1818-01-03	1818-01-03	None
1818-01-04	1818-01-04	None
1818-01-05	1818-01-05	None
...	...	...
1848-12-05	1848-12-05	None
1848-12-15	1848-12-15	None
1848-12-16	1848-12-16	None
1848-12-19	1848-12-19	None
1848-12-22	1848-12-22	None

3247 rows × 2 columns

	ds	y
Date

# confirm
df_daily_model

	ds	y
Date
1818-01-01	1818-01-01	62.0
1818-01-02	1818-01-02	62.0
1818-01-03	1818-01-03	62.0
1818-01-04	1818-01-04	62.0
1818-01-05	1818-01-05	62.0
...	...	...
2022-04-26	2022-04-26	132.0
2022-04-27	2022-04-27	132.0
2022-04-28	2022-04-28	135.0
2022-04-29	2022-04-29	107.0
2022-04-30	2022-04-30	51.0

74630 rows × 2 columns

# plot target vs index(date)
simple_plot_bulk(df_daily_model, 'y')

# A key point to remember here is: Since the null hypothesis assumes the presence of unit root, that is α=1, 
# the p-value obtained should be less than the significance level (say 0.05) in order to reject the null hypothesis. 
# Thereby, inferring that the series is stationary

# The ADF tests gives the following results – test statistic, p-value and the critical value at 1%, 5% , and 
# 10% confidence intervals.
adf_test_show(df_daily_model, 'y')

Results of Dickey-Fuller Test:
Test Statistic                -7.934017e+00
p-value                        3.452102e-12
#Lags Used                     6.300000e+01
Number of Observations Used    7.456600e+04
Critical Value (1%)           -3.430438e+00
Critical Value (5%)           -2.861579e+00
Critical Value (10%)          -2.566791e+00
dtype: float64
Conclusion
3.452102000963004e-12
Reject the null hypothesis: Stationary

# If Test statistic > Critical Value and p-value > 0.05 – Fail to Reject Null Hypothesis(HO) i.e., 
# time series does not have a unit root, meaning it is trend stationary.
kpss_test(df_daily_model['y'])

Results of KPSS Test:
Test Statistic             0.845332
p-value                    0.010000
#Lags Used               155.000000
Critical Value (10%)       0.347000
Critical Value (5%)        0.463000
Critical Value (2.5%)      0.574000
Critical Value (1%)        0.739000
dtype: float64
Conclusion
0.01
Reject the null hypothesis: Non-Stationary

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\statsmodels\tsa\stattools.py:2018: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is smaller than the p-value returned.

  warnings.warn(

ADF concludes stationary and KPSS concludes non-stationary – The series is difference stationary. Differencing is to be used to make series stationary. Then the differenced series is checked for stationarity.

FBProphet

Simple model

# Python
m_1 = Prophet(daily_seasonality=True)
m_1.fit(df_daily_model)
future = m_1.make_future_dataframe(365, freq='D')
forecast = m_1.predict(future)
fig = m_1.plot(forecast)

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)

# Python
m = Prophet(daily_seasonality=True, seasonality_mode='multiplicative')
m.fit(df_daily_model)
future = m.make_future_dataframe(365, freq='D')
forecast = m.predict(future)
fig = m.plot(forecast)

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)

Simple Custom Model

fb_prophet_model, future_dates_1, forcast_1, future_dates_2, forcast_2, future_dates_3, forcast_3 = simple_prophet_model(df_daily_model, 100, 200, 365, 'D', True, True)

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	11_yearly	11_yearly_lower	11_yearly_upper	daily	...	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yearly	yearly_lower	yearly_upper	additive_terms	additive_terms_lower	additive_terms_upper	yhat
74725	2022-08-04	4.883613	-36.550437	104.721594	4.883613	4.883613	-0.215524	-0.215524	-0.215524	5.638213	...	5.295590	5.295590	5.295590	-0.063153	-0.063153	-0.063153	0.0	0.0	0.0	30.745228
74726	2022-08-05	4.882721	-42.216390	91.049521	4.882721	4.882721	-0.205907	-0.205907	-0.205907	5.638213	...	5.389570	5.389570	5.389570	-0.021218	-0.021218	-0.021218	0.0	0.0	0.0	31.198487
74727	2022-08-06	4.881828	-35.882377	98.472239	4.881828	4.881828	-0.196506	-0.196506	-0.196506	5.638213	...	5.544288	5.544288	5.544288	0.022021	0.022021	0.022021	0.0	0.0	0.0	31.948092
74728	2022-08-07	4.880936	-35.774623	104.828273	4.880936	4.880936	-0.187325	-0.187325	-0.187325	5.638213	...	5.633946	5.633946	5.633946	0.068384	0.068384	0.068384	0.0	0.0	0.0	32.379863
74729	2022-08-08	4.880043	-40.195230	106.189655	4.880043	4.880043	-0.178364	-0.178364	-0.178364	5.638213	...	5.660128	5.660128	5.660128	0.118902	0.118902	0.118902	0.0	0.0	0.0	32.501714

5 rows × 25 columns

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	11_yearly	11_yearly_lower	11_yearly_upper	daily	...	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yearly	yearly_lower	yearly_upper	additive_terms	additive_terms_lower	additive_terms_upper	yhat
74825	2022-11-12	4.794357	-32.720362	100.703689	4.794357	4.794357	0.428085	0.428085	0.428085	5.638213	...	6.246252	6.246252	6.246252	0.075377	0.075377	0.075377	0.0	0.0	0.0	34.741116
74826	2022-11-13	4.793464	-32.705797	106.804435	4.793464	4.793464	0.442374	0.442374	0.442374	5.638213	...	6.313469	6.313469	6.313469	0.077658	0.077658	0.077658	0.0	0.0	0.0	35.056850
74827	2022-11-14	4.792571	-33.376521	106.315543	4.792571	4.792571	0.456916	0.456916	0.456916	5.638213	...	6.283724	6.283724	6.283724	0.062245	0.062245	0.062245	0.0	0.0	0.0	34.907765
74828	2022-11-15	4.791679	-37.992316	107.894671	4.791679	4.791679	0.471706	0.471706	0.471706	5.638213	...	6.300069	6.300069	6.300069	0.029609	0.029609	0.029609	0.0	0.0	0.0	34.979585
74829	2022-11-16	4.790786	-39.404269	106.256542	4.790786	4.790786	0.486738	0.486738	0.486738	5.638213	...	6.212661	6.212661	6.212661	-0.017172	-0.017172	-0.017172	0.0	0.0	0.0	34.554319

5 rows × 25 columns

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	11_yearly	11_yearly_lower	11_yearly_upper	daily	...	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yearly	yearly_lower	yearly_upper	additive_terms	additive_terms_lower	additive_terms_upper	yhat
74990	2023-04-26	4.647083	-32.563947	107.406943	4.647083	4.647083	1.158339	1.158339	1.158339	5.638213	...	6.622952	6.622952	6.622952	-0.047523	-0.047523	-0.047523	0.0	0.0	0.0	35.424486
74991	2023-04-27	4.646190	-34.961674	103.234296	4.646190	4.646190	1.159529	1.159529	1.159529	5.638213	...	6.653652	6.653652	6.653652	-0.077550	-0.077550	-0.077550	0.0	0.0	0.0	35.560320
74992	2023-04-28	4.645297	-39.249298	105.458401	4.645297	4.645297	1.161124	1.161124	1.161124	5.638213	...	6.722202	6.722202	6.722202	-0.100946	-0.100946	-0.100946	0.0	0.0	0.0	35.871924
74993	2023-04-29	4.644405	-28.932427	110.396833	4.644405	4.644405	1.163125	1.163125	1.163125	5.638213	...	6.807319	6.807319	6.807319	-0.112740	-0.112740	-0.112740	0.0	0.0	0.0	36.260352
74994	2023-04-30	4.643512	-32.572702	108.273136	4.643512	4.643512	1.165534	1.165534	1.165534	5.638213	...	6.710430	6.710430	6.710430	-0.109527	-0.109527	-0.109527	0.0	0.0	0.0	35.803477

5 rows × 25 columns

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)

WARNING:matplotlib.font_manager:findfont: Font family ['Lucida Grande'] not found. Falling back to DejaVu Sans.

data_train, data_test = split(df_daily_model, 100)
plot_test_predict(data_test, forcast_1[-200:-100])

Train dates : 1818-01-01 00:00:00 --- 2022-01-20 00:00:00  (n=74530)
Test dates  : 2022-01-21 00:00:00 --- 2022-04-30 00:00:00  (n=100)

data_train, data_test = split(df_daily_model, 200)
plot_test_predict(data_test, forcast_2[-400:-200])

Train dates : 1818-01-01 00:00:00 --- 2021-10-12 00:00:00  (n=74430)
Test dates  : 2021-10-13 00:00:00 --- 2022-04-30 00:00:00  (n=200)

data_train, data_test = split(df_daily_model, 365)
plot_test_predict(data_test, forcast_3[-730:-365])

Train dates : 1818-01-01 00:00:00 --- 2021-04-30 00:00:00  (n=74265)
Test dates  : 2021-05-01 00:00:00 --- 2022-04-30 00:00:00  (n=365)

initial = df_daily_model.shape[0] / 2

period = initial / 4

horizon = initial / 2

prophet, forcast, cv_results = model_with_cv(df_daily_model, 'linear', 'D', 365, initial, period, horizon, 'days')

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
INFO:fbprophet:Making 2 forecasts with cutoffs between 1945-09-14 18:00:00 and 1971-03-31 12:00:00

  0%|          | 0/2 [00:00<?, ?it/s]

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)

# get metrics on model
get_performance_metrics_plot(cv_results)

INFO:fbprophet:Skipping MAPE because y close to 0

data_train, data_test = split(df_daily_model, 365)
plot_test_predict(data_test, forcast[-730:-365])

Train dates : 1818-01-01 00:00:00 --- 2021-04-30 00:00:00  (n=74265)
Test dates  : 2021-05-01 00:00:00 --- 2022-04-30 00:00:00  (n=365)

mean_absolute_error(np.array(data_test["y"]), np.array(forcast.yhat[-730:-365]))

46.36536549229937

mean_absolute_percentage_error(np.array(data_test["y"]), np.array(forcast.yhat[-730:-365]))

987269422804166.9

r2_score(np.array(data_test["y"]), np.array(forcast.yhat[-730:-365]))

-1.6442459546691945

data_train, data_test = split(df_daily_model, 365)

Train dates : 1818-01-01 00:00:00 --- 2021-04-30 00:00:00  (n=74265)
Test dates  : 2021-05-01 00:00:00 --- 2022-04-30 00:00:00  (n=365)

prophet_d_2, forcast_d_2, cv_results_d_2 = model_with_cv(data_train, 'logistic', 39, 30, 30, 'D', 365, initial, period, horizon, 'days', monthly=True, daily=True)

C:\Users\akame\AppData\Local\Temp\ipykernel_20692\1129956497.py:6: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  df['cap'] = 500
C:\Users\akame\AppData\Local\Temp\ipykernel_20692\1129956497.py:7: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  df['floor'] = 1
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
INFO:fbprophet:Making 2 forecasts with cutoffs between 1944-09-14 18:00:00 and 1970-03-31 12:00:00

  0%|          | 0/2 [00:00<?, ?it/s]

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)

# get metrics on model
get_performance_metrics_plot(cv_results_d_2)

INFO:fbprophet:Skipping MAPE because y close to 0

plot_test_predict(data_test, forcast_d_2[-365:])

mean_absolute_error(np.array(data_test["y"]), np.array(forcast.yhat[-365:]))

24.84008937761477

mean_absolute_percentage_error(np.array(data_test["y"]), np.array(forcast.yhat[-365:]))

5485344368687209.0

r2_score(np.array(data_test["y"]), np.array(forcast.yhat[-365:]))

-0.006560427364540544

Monthly

Data and brief EDA

# load in dataset
df_monthly = data_load("monthly", ['Year', 'Month', 'Decimal_year', 'Sunspot_number', 'Standard_deviation', 
          'Number_observations', 'Provisional_indicator'], 'MS')

# simple & quick EDA
quick_look(df_monthly)

# plot target vs index(date)
simple_plot_bulk(df_monthly, "Sunspot_number", 'Standard_deviation', 'Number_observations')

	Year	Month	Day	Decimal_year	Sunspot_number	Standard_deviation	Number_observations	Provisional_indicator	ds
Date
1749-01-01	1749	1	1	1749.042	96.7	-1.0	-1	1	1749-01-01
1749-02-01	1749	2	1	1749.123	104.3	-1.0	-1	1	1749-02-01
1749-03-01	1749	3	1	1749.204	116.7	-1.0	-1	1	1749-03-01
1749-04-01	1749	4	1	1749.288	92.8	-1.0	-1	1	1749-04-01
1749-05-01	1749	5	1	1749.371	141.7	-1.0	-1	1	1749-05-01

	Year	Month	Day	Decimal_year	Sunspot_number	Standard_deviation	Number_observations	Provisional_indicator	ds
Date
2021-12-01	2021	12	1	2021.958	67.5	15.6	845	1	2021-12-01
2022-01-01	2022	1	1	2022.042	54.0	12.9	1007	0	2022-01-01
2022-02-01	2022	2	1	2022.122	59.7	13.1	1044	0	2022-02-01
2022-03-01	2022	3	1	2022.204	78.5	13.9	1277	0	2022-03-01
2022-04-01	2022	4	1	2022.286	84.1	15.2	1237	0	2022-04-01

<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 3280 entries, 1749-01-01 to 2022-04-01
Freq: MS
Data columns (total 9 columns):
 #   Column                 Non-Null Count  Dtype         
---  ------                 --------------  -----         
 0   Year                   3280 non-null   int64         
 1   Month                  3280 non-null   int64         
 2   Day                    3280 non-null   int64         
 3   Decimal_year           3280 non-null   float64       
 4   Sunspot_number         3280 non-null   float64       
 5   Standard_deviation     3280 non-null   float64       
 6   Number_observations    3280 non-null   int64         
 7   Provisional_indicator  3280 non-null   int64         
 8   ds                     3280 non-null   datetime64[ns]
dtypes: datetime64[ns](1), float64(3), int64(5)
memory usage: 256.2 KB

None

	Year	Month	Day	Decimal_year	Sunspot_number	Standard_deviation	Number_observations	Provisional_indicator
count	3280.000000	3280.000000	3280.0	3280.000000	3280.000000	3280.000000	3280.000000	3280.000000
mean	1885.167073	6.495122	1.0	1885.664664	81.594329	5.567896	110.492988	0.998780
std	78.916744	3.453518	0.0	78.916547	67.805438	5.220310	234.964151	0.034906
min	1749.000000	1.000000	1.0	1749.042000	0.000000	-1.000000	-1.000000	0.000000
25%	1817.000000	3.000000	1.0	1817.350250	23.900000	-1.000000	-1.000000	1.000000
50%	1885.000000	6.000000	1.0	1885.665000	66.850000	5.300000	30.000000	1.000000
75%	1953.250000	9.000000	1.0	1953.979000	122.400000	9.400000	31.000000	1.000000
max	2022.000000	12.000000	1.0	2022.286000	398.200000	23.500000	1587.000000	1.000000

# distribution of values
plot_kde(['Sunspot_number'], df_monthly['Sunspot_number'])

Model

# extract y
df_monthly_model = extract_df(df_monthly, 'Sunspot_number', 'y', 'ds')

# take a look at the data
display(df_monthly_model.head())
display(df_monthly_model.tail())

	ds	y
Date
1749-01-01	1749-01-01	96.7
1749-02-01	1749-02-01	104.3
1749-03-01	1749-03-01	116.7
1749-04-01	1749-04-01	92.8
1749-05-01	1749-05-01	141.7

	ds	y
Date
2021-12-01	2021-12-01	67.5
2022-01-01	2022-01-01	54.0
2022-02-01	2022-02-01	59.7
2022-03-01	2022-03-01	78.5
2022-04-01	2022-04-01	84.1

# median fill
df_monthly_model = handle_missing(df_monthly_model)

	ds	y
Date

	ds	y
Date

# confirm
df_monthly_model

	ds	y
Date
1749-01-01	1749-01-01	96.7
1749-02-01	1749-02-01	104.3
1749-03-01	1749-03-01	116.7
1749-04-01	1749-04-01	92.8
1749-05-01	1749-05-01	141.7
...	...	...
2021-12-01	2021-12-01	67.5
2022-01-01	2022-01-01	54.0
2022-02-01	2022-02-01	59.7
2022-03-01	2022-03-01	78.5
2022-04-01	2022-04-01	84.1

3280 rows × 2 columns

# plot target vs index(date)
simple_plot_bulk(df_monthly_model, 'y')

# A key point to remember here is: Since the null hypothesis assumes the presence of unit root, that is α=1, 
# the p-value obtained should be less than the significance level (say 0.05) in order to reject the null hypothesis. 
# Thereby, inferring that the series is stationary

# The ADF tests gives the following results – test statistic, p-value and the critical value at 1%, 5% , and 
# 10% confidence intervals.
adf_test_show(df_monthly_model, 'y')

Results of Dickey-Fuller Test:
Test Statistic                -1.056965e+01
p-value                        7.361427e-19
#Lags Used                     2.800000e+01
Number of Observations Used    3.251000e+03
Critical Value (1%)           -3.432363e+00
Critical Value (5%)           -2.862429e+00
Critical Value (10%)          -2.567243e+00
dtype: float64
Conclusion
7.3614268702497105e-19
Reject the null hypothesis: Stationary

# If Test statistic > Critical Value and p-value > 0.05 – Fail to Reject Null Hypothesis(HO) i.e., 
# time series does not have a unit root, meaning it is trend stationary.
kpss_test(df_monthly_model['y'])

Results of KPSS Test:
Test Statistic            0.099185
p-value                   0.100000
#Lags Used               36.000000
Critical Value (10%)      0.347000
Critical Value (5%)       0.463000
Critical Value (2.5%)     0.574000
Critical Value (1%)       0.739000
dtype: float64
Conclusion
0.1
DO NOT Reject the null hypothesis: Stationary

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\statsmodels\tsa\stattools.py:2022: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is greater than the p-value returned.

  warnings.warn(

FBProphet

# Python
m_m_1 = Prophet()
m_m_1.fit(df_monthly_model)
future = m_m_1.make_future_dataframe(9, freq='MS')
forecast = m_m_1.predict(future)
fig = m_m_1.plot(forecast)

INFO:fbprophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.
INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)

# Python
m_m_1 = Prophet(seasonality_mode='multiplicative')
m_m_1.fit(df_monthly_model)
future = m_m_1.make_future_dataframe(9, freq='MS')
forecast = m_m_1.predict(future)
fig = m_m_1.plot(forecast)

INFO:fbprophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.
INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)

m_fb_prophet_model, m_future_dates_1, m_forcast_1, m_future_dates_2, m_forcast_2, m_future_dates_3, m_forcast_3 = simple_prophet_model(m, df_monthly_model, 1, 6, 9, 'MS', False, True)

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	11_yearly	11_yearly_lower	11_yearly_upper	monthly	...	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yearly	yearly_lower	yearly_upper	additive_terms	additive_terms_lower	additive_terms_upper	yhat
3276	2022-01-01	7.712741	9.258132	122.322916	7.712741	7.712741	-1.814034	-1.814034	-1.814034	3.783418	...	8.193172	8.193172	8.193172	6.223788	6.223788	6.223788	0.0	0.0	0.0	70.904556
3277	2022-02-01	7.698902	14.532414	129.185346	7.698902	7.698902	-1.065609	-1.065609	-1.065609	3.090523	...	8.367016	8.367016	8.367016	6.342103	6.342103	6.342103	0.0	0.0	0.0	72.115739
3278	2022-03-01	7.686402	-17.568596	103.106793	7.686402	7.686402	-0.611406	-0.611406	-0.611406	-0.744174	...	4.499964	4.499964	4.499964	5.855544	5.855544	5.855544	0.0	0.0	0.0	42.274936
3279	2022-04-01	7.672563	-9.812172	106.386054	7.672563	7.672563	-0.584456	-0.584456	-0.584456	-0.193003	...	4.915622	4.915622	4.915622	5.693081	5.693081	5.693081	0.0	0.0	0.0	45.387979
3280	2022-05-01	7.659170	-17.820381	98.630554	7.659170	7.659170	-0.857793	-0.857793	-0.857793	-0.744174	...	4.157460	4.157460	4.157460	5.759426	5.759426	5.759426	0.0	0.0	0.0	39.501861

5 rows × 22 columns

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	11_yearly	11_yearly_lower	11_yearly_upper	monthly	...	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yearly	yearly_lower	yearly_upper	additive_terms	additive_terms_lower	additive_terms_upper	yhat
3281	2022-06-01	7.645331	-14.477241	95.985738	7.645331	7.645331	-1.034267	-1.034267	-1.034267	-0.193003	...	4.624787	4.624787	4.624787	5.852058	5.852058	5.852058	0.0	0.0	0.0	43.003360
3282	2022-07-01	7.631939	-18.036132	95.325363	7.631939	7.631939	-0.900859	-0.900859	-0.900859	-0.744174	...	4.393499	4.393499	4.393499	6.038531	6.038531	6.038531	0.0	0.0	0.0	41.162851
3283	2022-08-01	7.618099	-1.986724	107.034833	7.618099	7.618099	-0.615256	-0.615256	-0.615256	-0.193003	...	5.561731	5.561731	5.561731	6.369989	6.369989	6.369989	0.0	0.0	0.0	49.987917
3284	2022-09-01	7.604260	15.554102	123.760922	7.604260	7.604260	-0.441217	-0.441217	-0.441217	2.126176	...	8.046423	8.046423	8.046423	6.361464	6.361464	6.361464	0.0	0.0	0.0	68.791359
3285	2022-10-01	7.590868	-0.683231	109.302396	7.590868	7.590868	-0.351583	-0.351583	-0.351583	-0.193003	...	5.718765	5.718765	5.718765	6.263351	6.263351	6.263351	0.0	0.0	0.0	51.001257

5 rows × 22 columns

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	11_yearly	11_yearly_lower	11_yearly_upper	monthly	...	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yearly	yearly_lower	yearly_upper	additive_terms	additive_terms_lower	additive_terms_upper	yhat
3284	2022-09-01	7.604260	9.359481	125.649261	7.604260	7.604260	-0.441217	-0.441217	-0.441217	2.126176	...	8.046423	8.046423	8.046423	6.361464	6.361464	6.361464	0.0	0.0	0.0	68.791359
3285	2022-10-01	7.590868	-5.036902	109.436941	7.590868	7.590868	-0.351583	-0.351583	-0.351583	-0.193003	...	5.718765	5.718765	5.718765	6.263351	6.263351	6.263351	0.0	0.0	0.0	51.001257
3286	2022-11-01	7.577029	11.566874	126.982644	7.577029	7.577029	-0.040925	-0.040925	-0.040925	2.126176	...	7.981532	7.981532	7.981532	5.896282	5.896282	5.896282	0.0	0.0	0.0	68.053325
3287	2022-12-01	7.563636	-2.527021	117.348963	7.563636	7.563636	0.626989	0.626989	0.626989	-0.193003	...	6.572697	6.572697	6.572697	6.138712	6.138712	6.138712	0.0	0.0	0.0	57.277126
3288	2023-01-01	7.549797	20.323768	136.364790	7.549797	7.549797	1.429848	1.429848	1.429848	2.126176	...	9.491285	9.491285	9.491285	5.935261	5.935261	5.935261	0.0	0.0	0.0	79.207070

5 rows × 22 columns

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)

data_train, data_test = split(df_monthly_model, 9)
plot_test_predict(data_test, m_forcast_3[-18:-9])

Train dates : 1749-01-01 00:00:00 --- 2021-07-01 00:00:00  (n=3271)
Test dates  : 2021-08-01 00:00:00 --- 2022-04-01 00:00:00  (n=9)

mean_absolute_error(np.array(data_test["y"]), np.array(m_forcast_3.yhat[-18:-9]))

24.929743205486098

mean_absolute_percentage_error(np.array(data_test["y"]), np.array(m_forcast_3.yhat[-18:-9]))

0.5882169812719303

r2_score(np.array(data_test["y"]), np.array(m_forcast_3.yhat[-18:-9]))

-1.0260166592047866

m_forcast_1

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	11_yearly	11_yearly_lower	11_yearly_upper	monthly	...	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yearly	yearly_lower	yearly_upper	additive_terms	additive_terms_lower	additive_terms_upper	yhat
0	1749-01-01	7.680267	78.756511	193.134060	7.680267	7.680267	3.750674	3.750674	3.750674	5.610723	...	16.167483	16.167483	16.167483	6.806086	6.806086	6.806086	0.0	0.0	0.0	131.850853
1	1749-02-01	7.687117	61.625647	173.917351	7.687117	7.687117	3.549675	3.549675	3.549675	3.509333	...	14.209961	14.209961	14.209961	7.150954	7.150954	7.150954	0.0	0.0	0.0	116.920749
2	1749-03-01	7.693304	64.412086	175.885274	7.693304	7.693304	3.859887	3.859887	3.859887	3.575272	...	14.538621	14.538621	14.538621	7.103462	7.103462	7.103462	0.0	0.0	0.0	119.543334
3	1749-04-01	7.700154	79.862999	190.486533	7.700154	7.700154	4.431025	4.431025	4.431025	4.683129	...	16.677860	16.677860	16.677860	7.563705	7.563705	7.563705	0.0	0.0	0.0	136.122237
4	1749-05-01	7.706783	78.007180	195.502247	7.706783	7.706783	4.700524	4.700524	4.700524	3.575272	...	16.479652	16.479652	16.479652	8.203856	8.203856	8.203856	0.0	0.0	0.0	134.711878
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
3276	2022-01-01	7.712741	9.258132	122.322916	7.712741	7.712741	-1.814034	-1.814034	-1.814034	3.783418	...	8.193172	8.193172	8.193172	6.223788	6.223788	6.223788	0.0	0.0	0.0	70.904556
3277	2022-02-01	7.698902	14.532414	129.185346	7.698902	7.698902	-1.065609	-1.065609	-1.065609	3.090523	...	8.367016	8.367016	8.367016	6.342103	6.342103	6.342103	0.0	0.0	0.0	72.115739
3278	2022-03-01	7.686402	-17.568596	103.106793	7.686402	7.686402	-0.611406	-0.611406	-0.611406	-0.744174	...	4.499964	4.499964	4.499964	5.855544	5.855544	5.855544	0.0	0.0	0.0	42.274936
3279	2022-04-01	7.672563	-9.812172	106.386054	7.672563	7.672563	-0.584456	-0.584456	-0.584456	-0.193003	...	4.915622	4.915622	4.915622	5.693081	5.693081	5.693081	0.0	0.0	0.0	45.387979
3280	2022-05-01	7.659170	-17.820381	98.630554	7.659170	7.659170	-0.857793	-0.857793	-0.857793	-0.744174	...	4.157460	4.157460	4.157460	5.759426	5.759426	5.759426	0.0	0.0	0.0	39.501861

3281 rows × 22 columns

m_forcast_2

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	11_yearly	11_yearly_lower	11_yearly_upper	monthly	...	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yearly	yearly_lower	yearly_upper	additive_terms	additive_terms_lower	additive_terms_upper	yhat
0	1749-01-01	7.680267	75.856229	189.511027	7.680267	7.680267	3.750674	3.750674	3.750674	5.610723	...	16.167483	16.167483	16.167483	6.806086	6.806086	6.806086	0.0	0.0	0.0	131.850853
1	1749-02-01	7.687117	60.831443	174.914815	7.687117	7.687117	3.549675	3.549675	3.549675	3.509333	...	14.209961	14.209961	14.209961	7.150954	7.150954	7.150954	0.0	0.0	0.0	116.920749
2	1749-03-01	7.693304	57.643779	175.150421	7.693304	7.693304	3.859887	3.859887	3.859887	3.575272	...	14.538621	14.538621	14.538621	7.103462	7.103462	7.103462	0.0	0.0	0.0	119.543334
3	1749-04-01	7.700154	79.339628	190.766773	7.700154	7.700154	4.431025	4.431025	4.431025	4.683129	...	16.677860	16.677860	16.677860	7.563705	7.563705	7.563705	0.0	0.0	0.0	136.122237
4	1749-05-01	7.706783	73.409258	190.733222	7.706783	7.706783	4.700524	4.700524	4.700524	3.575272	...	16.479652	16.479652	16.479652	8.203856	8.203856	8.203856	0.0	0.0	0.0	134.711878
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
3281	2022-06-01	7.645331	-14.477241	95.985738	7.645331	7.645331	-1.034267	-1.034267	-1.034267	-0.193003	...	4.624787	4.624787	4.624787	5.852058	5.852058	5.852058	0.0	0.0	0.0	43.003360
3282	2022-07-01	7.631939	-18.036132	95.325363	7.631939	7.631939	-0.900859	-0.900859	-0.900859	-0.744174	...	4.393499	4.393499	4.393499	6.038531	6.038531	6.038531	0.0	0.0	0.0	41.162851
3283	2022-08-01	7.618099	-1.986724	107.034833	7.618099	7.618099	-0.615256	-0.615256	-0.615256	-0.193003	...	5.561731	5.561731	5.561731	6.369989	6.369989	6.369989	0.0	0.0	0.0	49.987917
3284	2022-09-01	7.604260	15.554102	123.760922	7.604260	7.604260	-0.441217	-0.441217	-0.441217	2.126176	...	8.046423	8.046423	8.046423	6.361464	6.361464	6.361464	0.0	0.0	0.0	68.791359
3285	2022-10-01	7.590868	-0.683231	109.302396	7.590868	7.590868	-0.351583	-0.351583	-0.351583	-0.193003	...	5.718765	5.718765	5.718765	6.263351	6.263351	6.263351	0.0	0.0	0.0	51.001257

3286 rows × 22 columns

m_forcast_3

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	11_yearly	11_yearly_lower	11_yearly_upper	monthly	...	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yearly	yearly_lower	yearly_upper	additive_terms	additive_terms_lower	additive_terms_upper	yhat
0	1749-01-01	7.680267	72.968868	187.754554	7.680267	7.680267	3.750674	3.750674	3.750674	5.610723	...	16.167483	16.167483	16.167483	6.806086	6.806086	6.806086	0.0	0.0	0.0	131.850853
1	1749-02-01	7.687117	59.532001	174.052215	7.687117	7.687117	3.549675	3.549675	3.549675	3.509333	...	14.209961	14.209961	14.209961	7.150954	7.150954	7.150954	0.0	0.0	0.0	116.920749
2	1749-03-01	7.693304	62.034269	180.854371	7.693304	7.693304	3.859887	3.859887	3.859887	3.575272	...	14.538621	14.538621	14.538621	7.103462	7.103462	7.103462	0.0	0.0	0.0	119.543334
3	1749-04-01	7.700154	78.882022	192.733134	7.700154	7.700154	4.431025	4.431025	4.431025	4.683129	...	16.677860	16.677860	16.677860	7.563705	7.563705	7.563705	0.0	0.0	0.0	136.122237
4	1749-05-01	7.706783	80.696468	190.157813	7.706783	7.706783	4.700524	4.700524	4.700524	3.575272	...	16.479652	16.479652	16.479652	8.203856	8.203856	8.203856	0.0	0.0	0.0	134.711878
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
3284	2022-09-01	7.604260	9.359481	125.649261	7.604260	7.604260	-0.441217	-0.441217	-0.441217	2.126176	...	8.046423	8.046423	8.046423	6.361464	6.361464	6.361464	0.0	0.0	0.0	68.791359
3285	2022-10-01	7.590868	-5.036902	109.436941	7.590868	7.590868	-0.351583	-0.351583	-0.351583	-0.193003	...	5.718765	5.718765	5.718765	6.263351	6.263351	6.263351	0.0	0.0	0.0	51.001257
3286	2022-11-01	7.577029	11.566874	126.982644	7.577029	7.577029	-0.040925	-0.040925	-0.040925	2.126176	...	7.981532	7.981532	7.981532	5.896282	5.896282	5.896282	0.0	0.0	0.0	68.053325
3287	2022-12-01	7.563636	-2.527021	117.348963	7.563636	7.563636	0.626989	0.626989	0.626989	-0.193003	...	6.572697	6.572697	6.572697	6.138712	6.138712	6.138712	0.0	0.0	0.0	57.277126
3288	2023-01-01	7.549797	20.323768	136.364790	7.549797	7.549797	1.429848	1.429848	1.429848	2.126176	...	9.491285	9.491285	9.491285	5.935261	5.935261	5.935261	0.0	0.0	0.0	79.207070

3289 rows × 22 columns

# do cv

Yearly

Data and brief EDA

# load in dataset
df_yearly = data_load("yearly", ['Year', 'Sunspot_number', 'Standard_deviation', 
          'Number_observations', 'Provisional_indicator'], 'YS')

# simple & quick EDA
quick_look(df_yearly)

# plot target vs index(date)
simple_plot_bulk(df_yearly, "Sunspot_number", 'Standard_deviation', 'Number_observations')

	Year	Month	Day	Sunspot_number	Standard_deviation	Number_observations	Provisional_indicator	ds
Date
1700-01-01	1700	1	1	8.3	-1.0	-1	1	1700-01-01
1701-01-01	1701	1	1	18.3	-1.0	-1	1	1701-01-01
1702-01-01	1702	1	1	26.7	-1.0	-1	1	1702-01-01
1703-01-01	1703	1	1	38.3	-1.0	-1	1	1703-01-01
1704-01-01	1704	1	1	60.0	-1.0	-1	1	1704-01-01

	Year	Month	Day	Sunspot_number	Standard_deviation	Number_observations	Provisional_indicator	ds
Date
2017-01-01	2017	1	1	21.7	2.5	11444	1	2017-01-01
2018-01-01	2018	1	1	7.0	1.1	12611	1	2018-01-01
2019-01-01	2019	1	1	3.6	0.5	12884	1	2019-01-01
2020-01-01	2020	1	1	8.8	4.1	14440	1	2020-01-01
2021-01-01	2021	1	1	29.6	7.9	15233	1	2021-01-01

<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 322 entries, 1700-01-01 to 2021-01-01
Freq: AS-JAN
Data columns (total 8 columns):
 #   Column                 Non-Null Count  Dtype         
---  ------                 --------------  -----         
 0   Year                   322 non-null    int32         
 1   Month                  322 non-null    int64         
 2   Day                    322 non-null    int64         
 3   Sunspot_number         322 non-null    float64       
 4   Standard_deviation     322 non-null    float64       
 5   Number_observations    322 non-null    int64         
 6   Provisional_indicator  322 non-null    int64         
 7   ds                     322 non-null    datetime64[ns]
dtypes: datetime64[ns](1), float64(2), int32(1), int64(4)
memory usage: 21.4 KB

None

	Year	Month	Day	Sunspot_number	Standard_deviation	Number_observations	Provisional_indicator
count	322.000000	322.0	322.0	322.000000	322.000000	322.000000	322.0
mean	1860.500000	1.0	1.0	78.365217	4.633540	1113.546584	1.0
std	93.097619	0.0	0.0	62.054638	5.274608	2574.732653	0.0
min	1700.000000	1.0	1.0	0.000000	-1.000000	-1.000000	1.0
25%	1780.250000	1.0	1.0	24.325000	-1.000000	-1.000000	1.0
50%	1860.500000	1.0	1.0	65.150000	4.150000	365.000000	1.0
75%	1940.750000	1.0	1.0	115.075000	8.850000	365.000000	1.0
max	2021.000000	1.0	1.0	269.300000	19.100000	15233.000000	1.0

# distribution of values
plot_kde(['Sunspot_number'], df_yearly['Sunspot_number'])

Model

# extract y
df_yearly_model = extract_df(df_yearly, 'Sunspot_number', 'y', 'ds')

# take a look at the data
display(df_yearly_model.head())
display(df_yearly_model.tail())

	ds	y
Date
1700-01-01	1700-01-01	8.3
1701-01-01	1701-01-01	18.3
1702-01-01	1702-01-01	26.7
1703-01-01	1703-01-01	38.3
1704-01-01	1704-01-01	60.0

	ds	y
Date
2017-01-01	2017-01-01	21.7
2018-01-01	2018-01-01	7.0
2019-01-01	2019-01-01	3.6
2020-01-01	2020-01-01	8.8
2021-01-01	2021-01-01	29.6

# median fill
df_yearly_model = handle_missing(df_yearly_model)

	ds	y
Date

	ds	y
Date

# confirm
df_yearly_model

	ds	y
Date
1700-01-01	1700-01-01	8.3
1701-01-01	1701-01-01	18.3
1702-01-01	1702-01-01	26.7
1703-01-01	1703-01-01	38.3
1704-01-01	1704-01-01	60.0
...	...	...
2017-01-01	2017-01-01	21.7
2018-01-01	2018-01-01	7.0
2019-01-01	2019-01-01	3.6
2020-01-01	2020-01-01	8.8
2021-01-01	2021-01-01	29.6

322 rows × 2 columns

# plot target vs index(date)
simple_plot_bulk(df_yearly_model, 'y')

# A key point to remember here is: Since the null hypothesis assumes the presence of unit root, that is α=1, 
# the p-value obtained should be less than the significance level (say 0.05) in order to reject the null hypothesis. 
# Thereby, inferring that the series is stationary

# The ADF tests gives the following results – test statistic, p-value and the critical value at 1%, 5% , and 
# 10% confidence intervals.
adf_test_show(df_yearly_model, 'y')

Results of Dickey-Fuller Test:
Test Statistic                  -3.106612
p-value                          0.026068
#Lags Used                       8.000000
Number of Observations Used    313.000000
Critical Value (1%)             -3.451416
Critical Value (5%)             -2.870819
Critical Value (10%)            -2.571714
dtype: float64
Conclusion
0.026067722399238862
Reject the null hypothesis: Stationary

# If Test statistic > Critical Value and p-value > 0.05 – Fail to Reject Null Hypothesis(HO) i.e., 
# time series does not have a unit root, meaning it is trend stationary.
kpss_test(df_yearly_model['y'])

Results of KPSS Test:
Test Statistic           0.23219
p-value                  0.10000
#Lags Used               7.00000
Critical Value (10%)     0.34700
Critical Value (5%)      0.46300
Critical Value (2.5%)    0.57400
Critical Value (1%)      0.73900
dtype: float64
Conclusion
0.1
DO NOT Reject the null hypothesis: Stationary

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\statsmodels\tsa\stattools.py:2022: InterpolationWarning: The test statistic is outside of the range of p-values available in the
look-up table. The actual p-value is greater than the p-value returned.

  warnings.warn(

FBProphet

df_yearly_model = df_yearly_model[100:]

# Python
y_m_m_1 = Prophet()
y_m_m_1.fit(df_yearly_model)
future = y_m_m_1.make_future_dataframe(9, freq='MS')
forecast = y_m_m_1.predict(future)
fig = y_m_m_1.plot(forecast)

INFO:fbprophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.
INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)

# Python
y_m_m_1 = Prophet(seasonality_mode='multiplicative')
y_m_m_1.fit(df_yearly_model)
future = y_m_m_1.make_future_dataframe(9, freq='MS')
forecast = y_m_m_1.predict(future)
fig = y_m_m_1.plot(forecast)

INFO:fbprophet:Disabling weekly seasonality. Run prophet with weekly_seasonality=True to override this.
INFO:fbprophet:Disabling daily seasonality. Run prophet with daily_seasonality=True to override this.
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)

y_fb_prophet_model, y_future_dates_1, y_forcast_1, y_future_dates_2, y_forcast_2, y_future_dates_3, y_forcast_3 = simple_prophet_model(m, df_yearly_model, 1, 10, 20, 'y', False, False)

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	11_yearly	11_yearly_lower	11_yearly_upper	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yearly	yearly_lower	yearly_upper	additive_terms	additive_terms_lower	additive_terms_upper	yhat
218	2018-01-01	293.041811	-42.872234	30.993260	293.041811	293.041811	0.472839	0.472839	0.472839	-1.025876	-1.025876	-1.025876	-1.498716	-1.498716	-1.498716	0.0	0.0	0.0	-7.582891
219	2019-01-01	294.294069	-46.275275	33.858983	294.294069	294.294069	0.467427	0.467427	0.467427	-1.022796	-1.022796	-1.022796	-1.490222	-1.490222	-1.490222	0.0	0.0	0.0	-6.708648
220	2020-01-01	295.546328	-24.021770	55.023074	295.546328	295.546328	0.523549	0.523549	0.523549	-0.951948	-0.951948	-0.951948	-1.475497	-1.475497	-1.475497	0.0	0.0	0.0	14.201545
221	2021-01-01	296.802017	-9.377513	69.865916	296.802017	296.802017	0.596289	0.596289	0.596289	-0.904633	-0.904633	-0.904633	-1.500922	-1.500922	-1.500922	0.0	0.0	0.0	28.305249
222	2021-12-31	298.050844	2.005792	82.010368	298.050844	298.050844	0.574787	0.574787	0.574787	-0.853015	-0.853015	-0.853015	-1.427802	-1.427802	-1.427802	0.0	0.0	0.0	43.808896

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	11_yearly	11_yearly_lower	11_yearly_upper	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yearly	yearly_lower	yearly_upper	additive_terms	additive_terms_lower	additive_terms_upper	yhat
227	2026-12-31	304.315566	-45.130584	33.892743	304.315566	304.315566	0.378173	0.378173	0.378173	-1.016994	-1.016994	-1.016994	-1.395167	-1.395167	-1.395167	0.0	0.0	0.0	-5.171436
228	2027-12-31	305.567825	-29.401218	50.137702	305.567825	305.567825	0.387177	0.387177	0.387177	-0.969790	-0.969790	-0.969790	-1.356967	-1.356967	-1.356967	0.0	0.0	0.0	9.231058
229	2028-12-31	306.823514	-57.646412	19.552771	306.823514	306.823514	0.398696	0.398696	0.398696	-1.055946	-1.055946	-1.055946	-1.454642	-1.454642	-1.454642	0.0	0.0	0.0	-17.165670
230	2029-12-31	308.075772	-46.920881	29.578128	308.075772	308.075772	0.398201	0.398201	0.398201	-1.029601	-1.029601	-1.029601	-1.427802	-1.427802	-1.427802	0.0	0.0	0.0	-9.119282
231	2030-12-31	309.328030	-28.717218	52.687273	309.328030	309.328030	0.431458	0.431458	0.431458	-0.963708	-0.963708	-0.963708	-1.395167	-1.395167	-1.395167	0.0	0.0	0.0	11.226026

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)

	ds	trend	yhat_lower	yhat_upper	trend_lower	trend_upper	11_yearly	11_yearly_lower	11_yearly_upper	multiplicative_terms	multiplicative_terms_lower	multiplicative_terms_upper	yearly	yearly_lower	yearly_upper	additive_terms	additive_terms_lower	additive_terms_upper	yhat
237	2036-12-31	316.848442	-191.747579	-114.424675	316.848441	316.848442	-0.025508	-0.025508	-0.025508	-1.480150	-1.480150	-1.480150	-1.454642	-1.454642	-1.454642	0.0	0.0	0.0	-152.134644
238	2037-12-31	318.100700	-112.282359	-30.080302	318.100700	318.100700	0.204442	0.204442	0.204442	-1.223360	-1.223360	-1.223360	-1.427802	-1.427802	-1.427802	0.0	0.0	0.0	-71.050916
239	2038-12-31	319.352958	-80.213256	2.779838	319.352958	319.352959	0.267632	0.267632	0.267632	-1.127535	-1.127535	-1.127535	-1.395167	-1.395167	-1.395167	0.0	0.0	0.0	-40.728622
240	2039-12-31	320.605216	-55.183305	26.777819	320.605216	320.605217	0.313737	0.313737	0.313737	-1.043230	-1.043230	-1.043230	-1.356967	-1.356967	-1.356967	0.0	0.0	0.0	-13.859753
241	2040-12-31	321.860906	-80.077528	-5.410814	321.860905	321.860906	0.324085	0.324085	0.324085	-1.130557	-1.130557	-1.130557	-1.454642	-1.454642	-1.454642	0.0	0.0	0.0	-42.021297

C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\forecaster.py:891: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead.
  components = components.append(new_comp)
C:\Users\akame\anaconda3\envs\env_full\lib\site-packages\fbprophet\plot.py:422: UserWarning: FixedFormatter should only be used together with FixedLocator
  ax.set_yticklabels(yticklabels)

data_train, data_test = split(df_yearly_model, 10)
plot_test_predict(data_test, y_forcast_2[-20:-10])

Train dates : 1800-01-01 00:00:00 --- 2011-01-01 00:00:00  (n=212)
Test dates  : 2012-01-01 00:00:00 --- 2021-01-01 00:00:00  (n=10)

mean_absolute_error(np.array(data_test["y"]), np.array(y_forcast_2.yhat[-20:-10]))

17.915335233607166

mean_absolute_percentage_error(np.array(data_test["y"]), np.array(y_forcast_2.yhat[-20:-10]))

0.816275044245692

r2_score(np.array(data_test["y"]), np.array(y_forcast_2.yhat[-20:-10]))

0.6223170586532639

data_train, data_test = split(df_yearly_model, 20)
plot_test_predict(data_test, y_forcast_3[-40:-20])

Train dates : 1800-01-01 00:00:00 --- 2001-01-01 00:00:00  (n=202)
Test dates  : 2002-01-01 00:00:00 --- 2021-01-01 00:00:00  (n=20)

mean_absolute_error(np.array(data_test["y"]), np.array(y_forcast_3.yhat[-40:-20]))

17.856170474371975

mean_absolute_percentage_error(np.array(data_test["y"]), np.array(y_forcast_3.yhat[-40:-20]))

0.847222161211042

r2_score(np.array(data_test["y"]), np.array(y_forcast_3.yhat[-40:-20]))

0.7179274229751886

initial = df_yearly_model.shape[0] / 2

period = initial / 4

horizon = initial / 2

prophet_y, forcast_y, cv_results_y = model_with_cv(df_daily_model, 'linear', 39, 30, 30, 'YS', 20, initial, period, horizon, 'days', monthly=False, daily=False)